That leaves one question then... is a graduate an expert? (What level is a graduate? And then what level is a journeyman?)
In the Babylon 5 setting, an "professional" telepath is someone who has reached a P5 rating. Apparently half of telepaths trying to reach that "level" burn out. At what level could a wizard be considered a professional? Perhaps when they can cast Fireball? (Note that some wizards would become experts far faster than others.)
Not sure there would be an objective answer there. It begs further questioning with respect to a spellcaster caste (doh) system; who is proficient, expert, master, etc? I'll take a cue from our world there and just let acumen adjudication be driven either by a specific metric or by some pre-determined frequency ratio within the population. With respect to D&D spellcasters, you're probably talking about spell levels (rather than just Arcana, etc, checks) and that will vary by setting. You can certainly have "able to successfully cast a 2nd level spell" as a binary pass/fail for graduates with post-graduate work requiring higher spell level proficiency.
I was never a fan of how psionics could fail that way. (You could fail a power check, or make it and watch an enemy save...) Presumably it's for gameplay :/
A wizard would "realistically" have a good chance of flubbing a spell. They could forget an arcane word, or mispronounce it, or their arthritis acted up, or they spilled their spell component pouch while ducking an arrow and need to pick those components up... I guess any "combat wizard" would be extensively trained in that kind of thing.
I agree. I didn't like it and its absence is most certainly to facilitate a better gameplay experience. I'm not condoning it. I'm just ruminating upon the paradigm and why the same logic wasn't extended to martial characters performing stunts in their primary discipline (martial combat/athletics).
"I want to jump on this giants back and stab him like <insert heroic archetype>."
"Oh man, that is way tough. Its going to require these two checks, a Strength to jump and a Dex to balance, each of which have a 40 % chance of failure...then roll to hit."
"Um, but this wizard can perfectly execute these Jimmy Hendrix riffs with his fingers plus his Luciano Pavarotti intonations in the midst of this stressful combat, while dodging arrows and hustling up this ridge to avoid the melee?"
"Yeah dude, like rock stars do all the time."
"And professional point guards dribble the ball off their foot in traffic at a 50 % clip?..."
"Whatever, roll your dice and fail already."
"Uh, I'll just hit him with my spear or bow or whatever..."